BERNOULLI’S EQUATION
Fluid Flow
Most techniques for evaluating head loss due to friction are empirical (based almost exclusively
on experimental evidence) and are based on a proportionality constant called the friction factor
(f), which will be discussed in the next section.
Example:
Extended Bernoulli
Water is pumped from a large reservoir to a point 65 feet higher than the reservoir. How
many feet of head must be added by the pump if 8000 lbm/hr flows through a 6-inch pipe
and the frictional head loss is 2 feet? The density of the fluid is 62.4 lbm/ft3, and the
cross-sectional area of a 6-inch pipe is 0.2006 ft2.
Solution:
To use the modified form of Bernoulli’s equation, reference points are chosen at the
surface of the reservoir (point 1) and at the outlet of the pipe (point 2). The pressure at
the surface of the reservoir is the same as the pressure at the exit of the pipe, i.e.,
atmospheric pressure. The velocity at point 1 will be essentially zero.
Using the equation for the mass flow rate to determine the velocity at point 2:
m2
rA2v2
v2
m2
rA2
v2
8000lbm
hr
62.4lbm
ft3
(0.2006 ft2)
v2
639
ft
hr
1 hr
3600 sec
v2
0.178
ft
sec
HT-03
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